Fermat Metrics

Symmetry

Antonio Masiello¹ 

[1] Department of Mechanics, Mathematics and Management, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy;

关键词: Finsler metrics;    stationary spacetimes;    Fermat principle;    light rays;    critical point theory;   

DOI  :  10.3390/sym13081422

来源: DOAJ

【 摘 要 】

In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.

【 授权许可】

Unknown